The methodology of resonant equiangular composite quantum gates

Guang Hao Low; Theodore J. Yoder; Isaac L. Chuang

doi:10.1103/PhysRevX.6.041067

paper

The methodology of resonant equiangular composite quantum gates

arXiv:1603.03996 · doi:10.1103/PhysRevX.6.041067

Abstract

The creation of composite quantum gates that implement quantum response functions $U^(θ)$ dependent on some parameter of interest $θ$ is often more of an art than a science. Through inspired design, a sequence of $L$ primitive gates also depending on $θ$ can engineer a highly nontrivial $U^(θ)$ that enables myriad precision metrology, spectroscopy, and control techniques. However, discovering new, useful examples of $U^(θ)$ requires great intuition to perceive the possibilities, and often brute-force to find optimal implementations. We present a systematic and efficient methodology for composite gate design of arbitrary length, where phase-controlled primitive gates all rotating by $θ$ act on a single spin. We fully characterize the realizable family of $U^(θ)$ , provide an efficient algorithm that decomposes a choice of $U^(θ)$ into its shortest sequence of gates, and show how to efficiently choose an achievable $U^(θ)$ that for fixed $L$ , is an optimal approximation to objective functions on its quadratures. A strong connection is forged with \emph{classical} discrete-time signal processing, allowing us to swiftly construct, as examples, compensated gates with optimal bandwidth that implement arbitrary single spin rotations with sub-wavelength spatial selectivity.

13 pages, 3 figures. v3: fixed typo in Eq.21

The methodology of resonant equiangular composite quantum gates

Abstract

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